Question

12. Consider steady, incompressible, parallel, laminar flow of a film of oil falling slowly down an infinite vertical wall as shown in the figure(Fig. P12a). The oil film thickness is h, and gravity acts in the negative z-direction (downward in the figure) There is no applied (forced) pressure driving the flow the oil falls by gravity alone. (1) Calculate the velocity field in the oi film and sketch the normalized velocity profile. And generate an expression for the volumetric flow rate per unit width (V/L) as function of p, H, h and g. (2) Compare your results to those of the same fluid falling between two infinite vertical walls with a free surface replacing the second wall (Fig. P12b). Ignore changes in the hydrostatic pressure of the surrounding air. x 4. x P Patm Oil film: Fixed wall Fixed wall Air Fluid: Fixed wall h (Fig. P12a) (Fig. P12b) foo foo

Answer 1

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